The origin is shifted to $(1, 2)$ . The equation $y^{2} - 8 x - 4 y + 12 = 0$ changes to $y^{2} = 4 a x$ , then $a =$

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Solution

The correct option is A $2$
Origin is shifted to $(1, 2)$
Then the point
$x = x + 1$ and $y = y + 2$
then shifting equation
$y^{2} - 3 x - 4 y + 12 = 0$
$(y + 2)^{2} - 8 (x \times 1) - 4 (y + 2) + 12 = 0$
$y^{2} + 4 + 4 y - 8 x - 8 - 4 y - 8 + 12 = 0$
$y^{2} - 8 x = 0$
$y^{2} = 8 x$
comparing this equation with
$y^{2} = 4 a x$ we get
$4 a = 8$
$a = 2$
Hence, this is the answer.

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Similar questions

(1, 2)

y^{2} - 8 x - 4 y + 12 = 0

Y^{2} + 4 a X = 0

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(1, 2),

y^{2} - 8 x - 4 y + 12 = 0

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